Displaying similar documents to “Bounded linear maps between (LF)-spaces.”

Factorization of Montel operators

S. Dierolf, P. Domański (1993)

Studia Mathematica

Similarity:

Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given. ...

Some aspects of the modern theory of Fréchet spaces.

Klaus D. Bierstedt, José Bonet (2003)

RACSAM

Similarity:

We survey some recent developments in the theory of Fréchet spaces and of their duals. Among other things, Section 4 contains new, direct proofs of properties of, and results on, Fréchet spaces with the density condition, and Section 5 gives an account of the modern theory of general Köthe echelon and co-echelon spaces. The final section is devoted to the developments in tensor products of Fréchet spaces since the negative solution of Grothendieck?s ?problème des topologies?. ...

Acyclic inductive spectra of Fréchet spaces

Jochen Wengenroth (1996)

Studia Mathematica

Similarity:

We provide new characterizations of acyclic inductive spectra of Fréchet spaces which improve the classical theorem of Palamodov and Retakh. It turns out that acyclicity, sequential retractivity (defined by Floret) and further strong regularity conditions (introduced e.g. by Bierstedt and Meise) are all equivalent. This solves a problem that was folklore since around 1970. For inductive limits of Fréchet-Montel spaces we obtain even stronger results, in particular, Grothendieck's problem...

Biduality in (LF)-spaces.

Klaus D. Bierstedt, José Bonet (2001)

RACSAM

Similarity:

En la Sección 1 se pueban resultados abstractos sobre preduales y sobre bidualidad de espacios (LF). Sea E = ind E un espacio (LF), ponemos H = ind H para una sucesión de subespacios de Fréchet H de E con H ⊂ H. Investigamos bajo qué condiciones el espacio E es canónicamente (topológicamente isomorfo a) el bidual inductivo (H')' o (incluso) al bidual fuerte de H. Los resultados abstractos se aplican en la Sección 2, especialmente a espacios (LF) ponderados de funciones holomorfas, pero...

Inductive limits of vector-valued sequence spaces.

José Bonet, Susanne Dierolf, Carmen Fernández (1989)

Publicacions Matemàtiques

Similarity:

Let L be a normal Banach sequence space such that every element in L is the limit of its sections and let E = ind E be a separated inductive limit of the locally convex spaces. Then ind L(E) is a topological subspace of L(E).

Density conditions in Fréchet and (DF)-spaces.

Klaus-Dieter. Bierstedt, José Bonet (1989)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

We survey our main results on the density condition for Fréchet spaces and on the dual density condition for (DF)-spaces (cf. Bierstedt and Bonet (1988)) as well as some recent developments.

Some normability conditions on Fréchet spaces.

Tosun Terzioglu, Dietmar Vogt (1989)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

We define two new normability conditions on Fréchet spaces and announce some related results.